Instructions: Use the given information to answer thequestions and interpret key features. Use any method ofgraphing or solving. Round to one decimal place, ifnecessary.The trajectory of a golf ball in a chip from the rough has aparabolic pattern. The height, in feet, of the ball is given bythe equation h(x) = -.25x² + 3.4x, where is thenumber of feet away from the golf club (along the ground)the ball is.The ball startsfeet above the ground.The ball reaches a+feet at a horizontal distance ofthe golf club it was hit with.The ball returns to the ground at aboutaway.height offeet away fromfeet

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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Using the concept of proportions and ratios on the similar triangles, the value of x is 48 units

Similar triangles are triangles that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are proportional. In other words, the ratios of the corresponding sides of similar triangles are equal.

The concept of similar triangles is based on the fundamental property that corresponding angles in similar shapes are equal, and the corresponding sides are proportional.

To determine the value of x, we can apply the concept of proportions and ratio on the similar triangle;

x / 36 = 64 / x

Cross multiplying both sides

x * x = 36 * 64

x² = 2304

x  = √2304

x = 48 units

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The simplified form of the expression is -24√35

Expression

Basically, an expression is the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the expression -6√7.4√5

Now, we have to simplify the expression.

While we looking into the given expression, we have identified that the expression is in the form of multiplication,

So, the first step in solving the expression is to group the similar element,

So, the grouped form of the expression is,

=> (-6 x 4).(√7 x √5)

Now, we have to perform the multiplication on it, then we get,

=> -24√35

Therefore, the simplified form of the expression is -24√35

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Answer:

\(\displaystyle a = \frac{8}{5}\).

Step-by-step explanation:

Two vectors \((x_1,\, y_1)\) and \((x_2,\, y_2)\) are parallel to one another if and only if the ratio between their corresponding components are equal:

\(\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}\).

Equivalently:

\(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\).

For the two vectors in this equation to be parallel to one another:

\(\displaystyle \frac{a}{4} = \frac{2}{5}\).

Solve for \(a\):

\(\displaystyle a = \frac{8}{5}\).

\(\displaystyle \frac{8}{5}\) would be the only valid value of \(a\); no other value would satisfy the \(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\) equation.

Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.

Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.

Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):

32 feet - 40 feet = -8 feet

It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level

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Answer:

-8 feet

Step-by-step explanation:

The expression (x²²)(x⁸)³ is equivalent to the given expression. Then, the value of p is 46.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is (x²²)(x⁸)³.

Using exponential laws we can solve the expression

(x²²)(x²⁴)   (∵\((a^m)^n=a^{m\times n}\))

= \(x^{22+24}\)  (∵\(a^m\times a^n=a^{m+n}\))

= x⁴⁶

The expression (x²²)(x⁸)³ is equivalent to \(x^p\)

So, x⁴⁶ = \(x^p\)

p=46 (∵ when bases are equal, then exponents will be equal)

Therefore, the value of p is 46.

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Answer:

D

Step-by-step explanation:

r/10 = -6

So r = -6x10

= -60

Remember that the coordinates of the points are written in the form (x,y), the first entry represents the distance over the horizontal axis and the second entry represents the distance over the vertical axis.

Plot the given points on the coordinate plane:

The length of the segment UV is 4, and the length of the segment UW is 9. Since the triangle VUW is a right triangle, use the Pythagorean Theorem to find the length of the segment VW:

Add the lengths of all the segments to find the perimeter of the triangle:

Therefore, to the nearest tenth, the perimeter of the triangle is 22.8.

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Step-by-step explanation:

has been given in the photo

Answer:

x= -3, x=7

Step-by-step explanation:

384 bc if 16 Is negative for get about the negative sign just add

a. There are 26 letters in the English alphabet, with two cases for each letter; 10 numerical characters in the range 0-9; and 5 special characters; thus a total of 26•2 + 10 + 5 = 67 characters.

Any character can be used more than once, so there are

67⁶ + 67⁷ + 67⁸ + 67⁹

or 27,618,753,243,839,080 total possible passwords.

b. If we require at least 1 special character, then there are 62 choices for each ordinary character we use and 5 for each special character.

Suppose we use a password of length 6. Then there are

62⁵•5¹ + 62⁴•5² + 62³•5³ + 62²•5⁴ + 62¹•5⁵ + 62⁰•5⁶

or

\(\displaystyle \sum_{k=1}^6 62^{6-k}\cdot5^k\)

We count the longer passwords in a similar fashion:

\(\displaystyle \sum_{m=6}^9 \left(\sum_{k=1}^m 62^{m-k}\cdot5^k\right)\)

or 1,206,930,268,794,100 total passwords

c. 1 second (s) is equal to 10⁶ microseconds (μs). If it takes 1 μs to try 1 password, then it would take

(1,206,930,268,794,100 passwords) • (1 μs / password) • (1 s / 10⁶ μs)

= 1,206,930,268.7941 s

= (1,206,930,268.7941 s) • (1 min / 60 s)

≈ 20,115,504.4799 min

≈ (20,115,504.4799 min) • (1 h / 60 min)

≈ 335,258.408 h

≈ (335,258.408 h) • (1 day / 24 h)

≈ 13,969.1003 days

≈ (13,969.1003 days) • (1 year / 365 days)

≈ 38.2715 years

Answer:

a) The function has a minimum value.

b) The minimum value of the function is -27.

c) The minimum value occurs at x=3.

Step-by-step explanation:

Answer:

22, 40, 40, and 41

Step-by-step explanation:

happy to help have a nice day

Answer:

There are 3 oatmeal cookies.

Step-by-step explanation:

Answer:

times up the outside bc we know the outside is the area

Answer:

y = 4x, y = 10x, etc.

Step-by-step explanation:

The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

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Answer: 32.83

heres the png with the math

Answer:

Those are both correct

Step-by-step explanation:

To solve for the triangle 12^2+10^2=c^2, and for the other question, you are correct because the hypotenuse is NEVER the shortest side.

The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Let "x" represent the width of the rectangular steel, then the length, which is 2meters less than triple the width, can be expressed as "3x-2".

The perimeter of the rectangular piece is 60meters.

The formula for the perimeter is the following:

Replace the formula with the expressions for the width and length and the given perimeter of the piece of steel:

w=x

l=3x-2

P=60

From this expression, you can determine the value of x.

-First, distribute the multiplication on the parentheses term

-Second, simplify the like terms and pass "-4" to the left side of the expression by applying the opposite operation "+4" to both sides of it

-Third, divide both sides by 8 to determine the value of x

The value of x is 8m, which means that the width of the piece of steel is 8m

To determine the length you just have to replace the expression by x=8

The length is 22m

The simplification of equation √8 + √98 - √64 is 9√2 - 8.

What is the simplification of the equation?

The process of writing an algebraic expression in the most effective and compact form without affecting the original expression's value is known as simplification. The procedure involves gathering related terms, which calls for adding or removing terms from an expression.

We have,

√8 + √98 - √64

By simplifying,

√8 = 2√2

√98 = √2 .7

√64 = 8

= 2√2 + √2 .7 - 8

= 9√2 - 8

Hence, the simplification of equation √8 + √98 - √64 is 9√2 - 8.

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Answer:

There are six possible committees if only men are chosen

Step-by-step explanation:

Here, we want to find the number of possible committees if only men are chosen

In this case, what will happen is that we shall be selecting the 5 people from the available 6 men

Mathematically, we can have this in 6C5 ways

which is read as 6 combination 5 ways

And that will be 6 ways

So there are six possible committees if only men are selected

Answer:

Round to the nearest whole dollar, the median weekly earnings of young adults with associate degrees in 2013 were $ 775.

Step-by-step explanation:

Given that in 2013 the median weekly earnings of young adults with bachelor degrees were $ 1108, and this represents a 43% increase over the weakly median earnings of young adults with associate degrees, to determine the median weekly earnings of the latter, the following must be done calculation:

X x 1.43 = 1108

X = 1108 / 1.43

X = 774.82

Therefore, round to the nearest whole dollar, the median weekly earnings of young adults with associate degrees in 2013 were $ 775.

The value of rate does he need to invest at in order to earn the $400 in interest is,

⇒ R = 4%

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Mr. Smith needs to earn $400 in interest on a $5000 investment.

And,  He can invest the money for two years.

Since, We know that;

Interest = PRT / 100

Substitute the given values, we get;

400 = 5000 × R × 2/100

⇒ 40,000 = 10,000R

⇒ R = 4

Thus, The value of rate does he need to invest at in order to earn the $400 in interest is,

⇒ R = 4%

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Answer:

Step-by-step explanation:

10,14,18

Answer:

this polygon has four sides shown here

Step-by-step explanation:

Answer: serbia

Step-by-step explanation: